What do you mean by two sets cross product

What do you mean by two sets cross product

Represents the direct product of two sets, also known as Cartesian product
The Descartes product of set a and B can be expressed as a × B = {(a, b) | a ∈ a, B ∈ B}. Generally speaking, this set is a set of ordinal pairs formed by pairwise collocation of elements in a and elements in B
For example, R × r = R & # 178; represents the set of points on the plane

Is vector square dot product or cross product ?
The square of vector a
Is vector a dot multiplied by vector a
Or vector a cross product vector a ?

Multiplication of vector a by vector a

Calculation of cross product of vector
|i j k|
|2 -3 1| =-7i-5j-k
|1 -2 3|
How does this work out,
It seems that the operation of coefficients before J is different from the other two,

I * (- 3) * 3 + J * 1 * 1 + k * 2 * (- 2) - k * (- 3) * 1 - J * 2 * 3 - I * 1 * (- 2) = - 7i-5j-ka11 * A22 * A33 + A12 * A23 * A31 + A13 * A21 * A32 - A12 * A21 * A33 - a11 * A23 * A32 you can see the rule one by one:)